4.1. Growth Kinetic Model and Parameter Estimation
The growth kinetic experiments using the pure SOB culture,
A. thiooxidans, were carried out under the extremely acidic conditions of pH 2 in this study. In low pH conditions, all the sulfide species exist in the non-ionized acidic form,
i.e., H
2S. In addition, a preliminary study on a mass balance analysis for the H
2S oxidation showed that greater than 95% of the introduced H
2S was converted to sulfate ion, SO
42−, even in a limited oxygen condition (data not shown), indicating that the production of intermediates such as elemental sulfur or thiosulfate was minimal by the SOB strain. Contrarily, several studies for biogas desulfurization have reported the accumulation of elemental sulfur as the end-product when oxygen was limited for the H
2S oxidation [
17,
19,
21]. Since the sulfate ion was the predominant end-product in this study, the production of the intermediates was not taken into account for the H
2S oxidation. The growth rate of the SOB strain and the H
2S removal rate were measured as a function of the concentrations of H
2S and oxygen introduced into the bioreactor.
First, the kinetic experiments were performed to measure the specific growth rate of the SOB by varying the concentration of H2S in the gas stream at 500, 1000, 1500, 2000, and 3000 ppm, while the DO concentration in the liquid phase was maintained at 5.9 ± 0.3 mg/L to minimize the oxygen effect. The corresponding concentrations of H2S in the liquid phase were measured as 0.16, 0.63, 1.79, 2.79, and 4.62 mg-S/L, respectively, in the presence of the active microbial culture. The liquid-phase abiotic concentrations of H2S calculated using the Henry’s law constant were 1.64, 3.27, 4.91, 6.54, and 9.82 mg-S/L, respectively, corresponding to the gaseous concentrations. The differences between the biotic and abiotic concentrations of H2S indicated that the SOB strain was sufficiently active to oxidize H2S in the acidic medium.
The specific growth rate of the SOB strain obtained in the H
2S loading experiments showed a typical Monod-type pattern, as illustrated in
Figure 1. A best-fit procedure was performed using the experimental data and Equation (6) without the oxygen effect, and the maximum specific growth rate, μm, was estimated as 0.037 h
−1, which was similar to the value of 0.041 h
−1 for
Thiobacillus sp. reported in the literature [
29]. Furthermore, the half saturation constant, K
S, was estimated to be 0.15 mg-S/L, which was very lower than the reported values of 8.9–11 mg/L for similar SOB species [
19,
26]. The low half saturation constant in this study indicates that the microbial strain grew well even at a low concentration of H
2S. These results also imply that the microbial activity of the SOB strain used in this study was maintained and even enhanced for the H
2S biodegradation in the extremely low pH.
Figure 1.
The specific growth rates of the SOB strain at different H2S concentrations in the liquid medium. The symbols show averaged experimental data with standard deviations, and the line illustrates model fitting.
Figure 1.
The specific growth rates of the SOB strain at different H2S concentrations in the liquid medium. The symbols show averaged experimental data with standard deviations, and the line illustrates model fitting.
The oxygen concentration in the liquid medium is an essential element for the aerobic biodegradation, and it must be considered with the main substrate,
i.e., H
2S, for the microbial growth kinetic relationship. Similarly, nitrification, the oxidation of ammonium to nitrate using DO by aerobic nitrifying bacteria, is an example for a dual substrate kinetic, and the nitrification and subsequent microbial growth did not take place at a threshold DO concentration of 0.5 mg/L [
25]. In order to determine both a threshold DO concentration and a DO effect on the kinetics for the H
2S oxidation by the SOB strain, growth rate experiments were also performed by varying the flowrate of oxygen introduced into the gas phase, while the experimental conditions including the pH and microbial density were kept the same as in the previous H
2S loading experiments, and the H
2S concentration introduced to the gas stream was maintained at approximately 500 ppm corresponding to the liquid-phase concentration of 0.18 ± 0.02 mg/L.
The specific growth rate of the SOB strain as a function of the DO concentration showed a sigmoidal shape as illustrated in
Figure 2. Growth and biodegradation of the SOB strain was not observed at a DO concentration of below 0.4 mg/L, the threshold concentration. The growth rate exponentially increased with increasing DO concentration in a range of 0.5–2.0 mg/L. At DO concentrations greater than 2.0 mg/L, the microbial growth rate remained unchanged with the maximum rate of 0.017 ± 0.003 h
−1. Consequently, the DO of 2.0 mg/L was the minimum concentration required to obtain the maximal activity and H
2S removal.
Figure 2.
The specific growth rates of the SOB strain as a function of the oxygen concentrations in the liquid medium. The symbols show averaged experimental data with standard deviations, and the line illustrates model fitting.
Figure 2.
The specific growth rates of the SOB strain as a function of the oxygen concentrations in the liquid medium. The symbols show averaged experimental data with standard deviations, and the line illustrates model fitting.
The microbial growth kinetic with the DO effect was estimated using Equation (6). The microbial growth kinetics for binary substrates has typically been described using the dual-Monod equation [
25,
26]; the dual-Monod kinetics cannot predict either the sigmoidal pattern or the low threshold where the microbial growth rate becomes almost zero. As a result, the modified Monod-Gompertz kinetic, Equation (5), was suggested in this study. The model simulation and the best-fit sequence using the modified Monod-Gompertz kinetic were performed, and the numerical result is illustrated as a solid line in
Figure 2. The half saturation constant of DO, K
O in the Monod-Gompertz equation represents an inflection point where the slope of the microbial growth rate changes from positive to negative; and it was estimated to be 1.10 mg/L.
The yield coefficient for the H
2S utilization, Y
X/S, is one of the important parameters for the kinetic model. Another bacterial growth experiment was performed at a DO concentration of 6.0 mg/L and an initial microbial density of 200 ± 20 mg-dry weight/L. The yield coefficient was calculated to be 0.093 mg-dry weight/mg-S using Equation (7), which was similar to another yield value of 0.09 mg/mg for an SOB strain reported in the literature [
26]. In cases of multiple, interacting substrates, the other yield coefficient for the secondary substrate can be estimated using that of the primary substrate [
25], and Equation (8) was derived and used to estimate the yield coefficient for oxygen, Y
X/O, at 0.732 mg/mg. All the kinetic model parameters estimated in this study are listed in
Table 1.
Table 1.
Kinetic model parameters used in this study.
Table 1.
Kinetic model parameters used in this study.
Parameters | Values | Bioreactors | Reference |
---|
Estimated | μmax | 0.037 | 1/h | this study |
KS | 0.15 | mg-S/L | this study |
KO | 1.10 | mg-O/L | this study |
YX/S | 0.093 | mg-dry weight/mg-S | this study |
YX/O | 0.732 | mg-dry weight/mg-O | this study |
Known | HS | 0.427 | - | [30] |
HO | 32.3 | - | [30] |
DS | 0.0000161 | cm2/s | [30] |
DO | 0.0000240 | cm2/s | [30] |
KLaO | 1.42 | 1/min | [24] |
4.2. Model Validation and Simulation
The microbial removal of H
2S in biogas requires DO at a concentration greater than the threshold, but the oxygen supply in the gas phase has an upper limit,
i.e., 6% by volume, due to economic and safety issues [
5]. Consequently, the appropriate oxygen concentration required for biogas desulfurization must be carefully selected to ensure the effective removal of H
2S under diverse operating conditions. In this study, the kinetic model was validated using the data from the short-term bioreactor experiments. Furthermore, the model simulation was used to determine the optimal oxygen concentration required at different gas retention times and influent H
2S concentrations.
4.2.1. Effects of Gas Retention Times (GRTs)
The experimental results obtained from the short-term bioreactor operation were used to evaluate the numerical model using the coupled mass balance Equations (10), (11), (12), and (13) and its parameters described above. The experimental and model simulation results for the H
2S oxidation as a function of the oxygen content in the influent gas stream was illustrated in the
Figure 3. In the short-term bioreactor experiments, the H
2S concentration in the influent gas stream was remained constant at 1000 ± 45 ppm, and the initial microbial density was 500 ± 20 mg/L, while three different GRTs of 1, 5, and 10 min were applied at the influent oxygen contents of 1% and 2%, respectively. At the oxygen content of 1% and the GRT of 1 min, the H
2S removal efficiency was less than 5%, indicating that the biological oxidation of H
2S was minimal. When the oxygen content in the gas stream increased to 2% while the other conditions remained unchanged, the H
2S removal efficiency increased slightly to approximately 20%. As expected, the longer GRT, the higher removal efficiency at the given oxygen contents. At the longest GRT of 10 min, the H
2S removal efficiencies were found to be 54% and 98% at the influent oxygen contents of 1% and 2%, respectively. These results imply that the oxygen supply be one of the most critical parameters for aerobic bio-desulfurization as the H
2S loading increases.
Figure 3.
Experimental data (symbols) and model simulation results (lines) at different gas retention times as a function of the influent oxygen content.
Figure 3.
Experimental data (symbols) and model simulation results (lines) at different gas retention times as a function of the influent oxygen content.
To determine the GRT required to meet the H
2S concentration in the effluent gas stream and the oxygen supply, the numerical simulation using the kinetic model was performed. In the model simulation, as the same as the experimental conditions, an influent concentration of H
2S of 1000 ppm and the initial microbial density of 500 mg/L were applied, and the H
2S removal efficiencies were calculated at the GRTs of 1, 3, 5, 7 and 10 min as a function of the oxygen content in the influent gas stream, as illustrated in
Figure 3. The model simulations agree well with the experimental results at the given conditions, indicating that the numerical model applied in this study was suitable for the prediction of the performance of the bioreactor using the SOB strain at the low pH condition.
Similarly to the experimental results, the model prediction shows that the H2S removal efficiency increased with increasing the GRT at a given oxygen content. To meet the regulatory standard for biogas utilization, e.g., the H2S concentration of 10 ppm in Korea, the minimum requirements of the oxygen supply in the influent gas stream were estimated to be 4.3, 3.1, 2.7 and 2.3% at the GRT of 3, 5, 7, and 10 min, respectively. Note that the regulatory H2S standard could not be met in the bioreactor operating at the GRT of 1 min, even at the oxygen concentration of 6% or higher. This indicates that the influent oxygen concentration should be controlled in a range of 2%–6% for the effective removal of H2S, and a GRT of more than 3 min needs to be selected to achieve the design purpose in this bioreactor configuration.
4.2.2. Effects of Microbial Density
The changes in H
2S removal efficiency at various microbial densities and influent oxygen contents were simulated, and the simulation results and experimental data are illustrated in
Figure 4. The experimental data was obtained from a bioreactor operating condition at the influent H
2S concentration of 1000 ppm and the GRT of 5 min. At the lowest microbial density of 100 mg/L simulated in this study, the H
2S removal efficiency greater than 99%,
i.e., the effluent H
2S concentration of 10 ppm, could not be met even at the highest oxygen contents of 6%. Therefore, the low microbial density was not feasible and applicable for the biological process to achieve the effective removal of H
2S in biogas. When the microbial density increased to 250 mg/L in the simulation, the H
2S removal efficiency increased, and the effluent H
2S concentration of 10 ppm would be achieved at the oxygen content of greater than 5%. At the microbial densities of higher than 500 mg/L, the changes of the H
2S removal efficiency were not substantial as a function of the oxygen content as shown in
Figure 4, and the effluent H
2S standard would be met at the oxygen content of 3% or higher.
Figure 4.
Experimental data (symbols) and model simulation results (lines) at different microbial densities as a function of the influent oxygen content.
Figure 4.
Experimental data (symbols) and model simulation results (lines) at different microbial densities as a function of the influent oxygen content.
4.2.3. Effects of Influent H2S Concentration
The H
2S concentration in biogas varies widely depending on the source of the anaerobic digestion. In this study, the H
2S removal efficiencies were numerically determined at the influent H
2S concentrations of 250, 500, 1000, 2500 and 5000 ppm as a function of the oxygen content introduced into the influent gas stream illustrated in
Figure 5a, while the other simulation parameters remained unchanged at the GRT of 5 min and the initial microbial density of 500 mg/L. Again, to meet the H
2S regulatory standard of 10 ppm in the effluent gas stream, the simulation estimated that the oxygen fractions of 2.6, 2.8, 3.2, and 4.2% (v/v) were required at the influent H
2S concentrations of 250, 500, 1000, and 2500 ppm, respectively. These results imply that the biological oxidation of H
2S at a concentration of less than 2500 ppm can occur easily when the gas stream is mixed with oxygen at a content less than 5% in this bioreactor operation. However, at the H
2S concentration of 5000 ppm, this biological method could not meet the regulatory standard for the effluent stream even when the oxygen content was increased to more than 6%, the practical guideline for biogas utilization. As a result, the operating conditions of the bioreactor in this study were not suitable for the removal of the high concentration of H
2S of more than 5000 ppm, and the gas retention time and/or the microbial density should be increased to achieve the required removal efficiency.
Figure 5.
Experimental data (symbols) and model simulation results (lines) of (a) the H2S removal efficiency and (b) dissolved oxygen concentration at different influent oxygen contents and H2S concentrations.
Figure 5.
Experimental data (symbols) and model simulation results (lines) of (a) the H2S removal efficiency and (b) dissolved oxygen concentration at different influent oxygen contents and H2S concentrations.
The DO concentrations in liquid phase at different H
2S and oxygen loading conditions were compared using the model simulations as illustrated in
Figure 5b. In cases of abiotic operation without the active SOB strain, the DO concentration in the liquid increased in a linear manner up to 2.0 mg/L in a range of the influent oxygen fraction from 0% and 5% as delineated as a dotted line in
Figure 5b. In the presence of the active SOB strain, the DO concentration decreased due to the biological utilization, and the amount of utilized oxygen increased as both the inlet H
2S and the biodegradation rate increased. It is interesting to note that, under the condition of an oxygen supply of less than 6% simulated in this study, the DO concentration in the bioreactor medium was always lower than 2.0 mg/L where the biodegradation kinetic rate was sensitive, as shown in
Figure 3.
Figure 6 is presented to show the simulation results on the effect of the oxygen supply in the gas stream on the effluent H
2S concentration. The horizontal dotted line represents the regulatory H
2S concentration of 10 ppm, and the vertical arrows indicate the highest inlet concentration of H
2S that can be treated at the given oxygen content. For instance, the highest concentration of H
2S to meet the regulatory standard was approximately 2000 ppm at an oxygen content of 5%. Comparatively, when the influent concentration of H
2S increases to more than 2500 ppm, the bioreactor required the oxygen supply at more than 10%, which was practically unsafe and infeasible. The same simulation results are also illustrated in
Figure 7, which shows the highest inlet concentration of H
2S that can be treated to meet the standard of 10 ppm as a function of the inlet oxygen content.
Figure 6.
Model simulation results of the H2S concentrations at the effluent stream at different influent H2S concentrations and oxygen contents.
Figure 6.
Model simulation results of the H2S concentrations at the effluent stream at different influent H2S concentrations and oxygen contents.
In order to determine an appropriate oxygen supply for design and practical purposes, the specific removal of H
2S normalized by the required oxygen concentration was calculated and given in
Figure 7 as the dotted line. At low oxygen supply conditions, the specific removal of H
2S,
i.e., the allowable H
2S concentration per oxygen, increased with increasing oxygen content.
Figure 7.
The highest inlet concentration of H2S and the specific removal rate of H2S as a function of the inlet oxygen content.
Figure 7.
The highest inlet concentration of H2S and the specific removal rate of H2S as a function of the inlet oxygen content.
The specific removal of H2S showed the highest value of approximately 400 ppm/%-O2 at the influent oxygen content of 4.9%. This value implies that the H2S biodegradation should be operated in the condition of an optimal oxygen supply, and the excess oxygen would not be efficiently utilized at an oxygen content of more than the optimal point. These simulation results can change depending on the bioreactor volume, GRT, and microbial density; nevertheless, the introduction of oxygen above the optimal concentration is not practically effective in the bioreactor because of the decline in oxygen efficiency.